Optimal Block Stacking

FeaturedOptimal Block Stacking

I am pleased to announce that Shahab Derhami, Jeff Smith and I have just had a manuscript accepted in International Journal of Production Research entitled, “Optimizing Space Utilization in Block Stacking Warehouses.” Congratulations especially to Shahab—this is the first paper from his dissertation research!

The origin of this paper was a consulting engagement Jeff and I had with a beverage manufacturer, in which pallets roll off a production line and then are stored for a time before shipping. The finished goods warehouse uses deep lane block stacking, as is common in many large lot, unit load handling environments. The company wanted to know how deep lanes should be to make the best use of space.

Space lost due to honeycombing

Block stacking warehouses waste space in two ways: aisles to allow lift truck travel and partially filled lanes, which another sku cannot occupy because it would block access to the sku already stored there. As explained in Bartholdi and Hackman’s textbook, each lane makes a contribution to both types of waste. If lanes are too shallow, then too much storage space is devoted to aisles; if too deep, then too much storage lane space is wasted. An optimal design balances this tradeoff.

The academic literature has well-known results for optimal lane depth in the case of instantaneous resupply, which is appropriate for warehouses storing product received from suppliers. Pallets for a particular sku arrive at the same time, so the production rate is “infinite.” A second assumption behind existing results is continuous demand, rather than discrete demand. Our paper relaxes both of these assumptions: production rate can be finite—even less than the rate of demand, and demand is discrete. (The production rate can be less than the rate of demand if demand is only intermittent. Imagine all demand for a particular sku happening only on Friday, for example.) The paper develops approximations for the optimal lane depths for block stacking areas with one or multiple skus.

The main insight we develop in the paper is that using the infinite production rate model in a finite production rate environment produces lane depths about twice as deep as they should be, but that the resulting loss of space is modest (less than about 2 percent). Said another way, the space utilization curve, as a function of lane depth, is quite flat.

However, shorter, optimal lanes means more aisles and therefore more flexibility with respect to travel for lift truck drivers or autonomous vehicles. The effects of lane depth on travel costs have not been considered in our work or in the literature.

We welcome your comments.


The Age of Excess Capacity

FeaturedThe Age of Excess Capacity

For the past several months I have been thinking about trends in the logistics industry and in the economy as a whole. The rate of innovation is so high right now that I have been unable to think categorically about it all. What I mean is, I would like to be able to see a news piece about a company with a great idea and think, “Right, that‘s another example of this.” My problem has been that I just haven’t been able to assemble a coherent list of “thises.” Today’s post is my attempt to define a “this” for the gig economy.

Before I get to my Organizing Principle, a personal story:  In 2004 I gave an INFORMS presentation that included a very unsatisfying conjecture I had worked unsuccessfully to prove for about three months. I was “sure” my method produced optimal solutions, and had worked both to prove the result and to disprove it by counterexample, all to no avail. Knowing the presentation would be attended by about thirty colleagues and Ph.D. students, I decided to make my claim (the conjecture) and then offer $100 to the first person who could disprove it. Assuming each person gave only 10 minutes of thought to it, I would get 5 hours of work and a proof (by counterexample) that my method was not optimal, all for $100—not bad; else, I would get the work for free.

After my talk, I was told that people were actively working on my problem in the elevator as they returned to their rooms. Alas, the next morning my friend Samir Amiouny produced a counterexample that led to a minor modification of my algorithm, which then produced his solution as well. Without knowing it, I had just used “the crowd” to solve a knotty technical problem.

I didn’t think in these terms at the time, but my experiment was successful because it tapped into the otherwise unused intellectual capacity of my audience. Had they not been given a nice little problem to think about, my audience might have left the presentation and engaged in something unproductive like small talk or going to coffee—instead of, you know, working on my problem! The experiment was also successful because the seminar itself served as a coordinating mechanism that gave a common understanding of the task and established the rules. Finally, I had offered them an incentive to work voluntarily on my problem, thereby selecting from the audience the most willing and motivated problem solvers.

It is important to note that I probably did not attract the most capable problem solvers, only the most willing and motivated. Had I offered $100,000 instead of $100, I suspect I would have attracted the efforts of the entire group, including the most capable problem solvers. The level of reward determines the capability of the talent pool.

And now to the gig economy at large. I might be the last to realize this, but it seems that the Organizing Principle around gig economy businesses is something like this:

Find excess capacity in resources, organizations, systems, and individuals and then create a coordinating mechanism that allows providers, for a price, to offer their capacity voluntarily and spontaneously.

In other words, there is a lot of excess capacity out there, if people and organizations are willing to make it available. We have entered The Age of Excess Capacity, in which resources can be productive much more of the time. Why hasn’t this been done in the past? We have lacked the coordinating mechanisms, a void now filled by apps and mobile computing. Now, some examples of Excess Capacity Businesses.

Uber is the most famous example of an Excess Capacity Business. The genius behind Uber was the realization that empty seats (unused capacity) fill the highways and streets of every city in the world, and the drivers of some of those seats might be willing to volunteer them to people needing a ride. Why was this never done before? Before Uber, there was no coordinating mechanism between the drivers and potential customers, so customers could not participate; and there was no reward, so drivers had no incentive to participate. Note the key elements: a coordinating mechanism and a reward for providers.

AirBnB is also an Excess Capacity Business, based on the observation that an empty bedroom is “unused storage capacity” for people. Every day millions of people drive past empty residential bedrooms to pay $100 per night to stay in sterile hotel rooms. Enter a coordinating mechanism (AirBnB software) and a reward for the provider (rent), and presto—a billion dollar company.

Maketime is an Excess Capacity Business in manufacturing that attempts to match customers with idle machines (via software, the coordinating mechanism), giving manufacturers higher rates of utilization on their existing assets and therefore a higher rate of return (reward).

Co-creation in product development (e.g., FirstBuild) taps excess mental capacity of engineers, industrial designers, makers, and hobbyists. Think about how many brilliant people waste intellectual energy every night as they watch YouTube videos and play video games! FirstBuild offers the coordinating mechanism (co-creation software platform) and reward to its providers, who retain the IP on their inventions.

For all of these businesses, providers must be volunteers and able to withdraw their service spontaneously because, presumably, the asset was not purchased with a gig economy in mind. I didn’t buy a car so I could be an Uber driver, and I don’t have an extra bedroom so I can let it out on AirBnB. Some might choose to do these things, but the business models do not assume this is the case.

Now for some more interesting cases. What about parking lots, which are mostly empty? Should a shopping mall rent out portions of its parking lot at night to enable, say, real time crossdocking of freight in an urban environment? Doing so at night seems pretty safe, but what about during the day?

How about your garage? Why not build a company called AirDC that connects pallets with pallet positions in residential areas in real time? Think about the value of a highly distributed, virtual distribution center in downtown Atlanta. Just as Uber operates a taxi service without cars, AirDC would offer a distribution center with no building.

And my favorite: railroad tracks. What do you imagine is the utilization of an inch of railroad track? 0.001 percent? Surely we can do better!

To review: the unifying idea—the Organizing Principle—among all of these businesses is:

  • Recognition of unused capacity. Why is it just sitting there when others might be able to use it right now?
  • A coordinating mechanism, usually via software. Uber and AirBnB, for example, are software companies, not transportation or hotel companies. Why isn’t the resource being used right now? How can we connect potential users with idle resources?
  • Voluntary participation by providers. Unlike contracts, which bind seller and buyer, resources in an Excess Capacity Business can choose to enter or leave service at their leisure. By definition, they are offering marginal capacity, and therefore must be allowed to withdraw for a time, as, for example, when they are at full utilization (e.g., in-laws encroaching on your AirBnB cash flow).

In closing, I can’t help but note that the growth potential of an Excess Capacity Business is limited by…the amount of excess capacity! In these heady days of $60B Uber valuations (more than Ford and GM), let us not forget that Uber and its competitors are at the mercy of a public willing to spend its free time driving a cab around town. That pool is limited.


GridStore paper award

FeaturedGridStore paper award
I am happy to report that my colleagues Kai Furmans, Zäzilia Seibold, Onur Uludag and I recently received the 2015 Best Application Paper Award from IEEE Transactions on Automation Science and Engineering for our paper, GridStore: A Puzzle-Based Storage System with Decentralized Control. Zäzilia and Onur, in particular, made outstanding contributions to this work. Onur went on to extend these ideas in his GridPick system, and Zäzilia is going further still with her work on GridSorter and other things.
Below is the letter Zäzilia read on our behalf while accepting the award at the conference in Sweden:
On behalf of Drs. Furmans, Gue, and Uludag, we regret that we could not join you today!
We should say at the outset that the research behind this paper was collaborative in the fullest sense, with each author making unique and valuable contributions along the way.  But the paper represents more than just collaboration; it represents two research teams in two countries, with two previously independent streams of research, creating something neither team could have imagined without the other.  Gue and Uludag began with prior research in puzzle-based storage systems. Furmans and Seibold began with previous research in decentralized control of conveyor modules.  The research in this paper is a gratifying combination of the two—decentralized control of a puzzle-based storage system.
The ideas in this paper have already been extended in our own research, and it is our hope that others will move them even further.  We believe that decentralized control represents an attractive means of dealing with the extreme complexity that characterizes so many logistics systems today.  We hope that our paper will become just a small contribution to our understanding of these systems.  We are also pleased to report that a working prototype of the GridStore system has been built and is on display at the Institute for Material Handling and Logistics in Karlsruhe.  It is our hope that, someday, we will see these systems working in industry.
We would like to thank the editorial team at IEEE Transactions on Automation Science and Engineering for helpful comments during the publication process.  We also thank the U.S. National Science Foundation for providing the financial support that made this work possible.
Many thanks and best regards from Germany and the United States.  Enjoy your time in Sweden!
Kai Furmans
Kevin Gue
Onur Uludag

GridStore implemented

FeaturedGridStore implemented

One of the most satisfying parts of this job is seeing others take your work and go further. In this case, Benedikt Fuß, who spent time with me at Auburn and who is now a research associate at the Institute for Material Handling and Logistics at Karlsruhe Institute of Technology, has improved the GridStore algorithm by adding asynchronous control.

As originally conceived, GridStore operates in stepwise fashion, with each conveyor module deciding its action and taking it according to a shared clock. An admitted weaknesses of that work was our failure to explain exactly how synchronization would be implemented in modules without a centralized controller. Enter Benedikt’s asynchronous modification, in which modules operate independently and without a common clock, yet seem to synchronize on their own. Notice the slight variations of timing among the modules in the video below:

Do I even need to say how satisfying it is to see this work implemented in a real system? Here’s hoping these ideas someday are applied in industry. Then, I retire.

Logistics Automation and Us

FeaturedLogistics Automation and Us

Several years ago I began telling my children that I thought the greatest challenge for their generation was sensibly integrating technology into everyday life. It seemed at the time (and I continue to believe) that the blind adoption of rapidly advancing technology would have unknown and possibly deleterious effects on the human condition. Sounds like the subject for a nice book, eh? Alas, Nicholas Carr has beaten me to it with The Glass Cage: Automation and Us. The Glass Cage: Automation and Us

While recognizing the industrial and social benefits of automation, Carr points out that our inventions no longer help us accomplish work, but rather do the work for us. If the work is mindless or backbreaking, so much the better, but technology now threatens to rob us of many of the experiences that make us human. As I have written elsewhere, this point really resonates with me. I am reminded of a rhetorical question posed by a friend several years ago: “Why do I have to remember anything, when I can just look it up?” That is a serious question. The answer, of course, is that remembering—knowing—is a critical part of what makes us human. Machines look things up; humans know.

The challenge is to build technology that relieves man of the burden of work without robbing him of the satisfaction of work. Here Carr gives a huge shout out to the human factors research community, which knows a great deal about the interaction of humans and their machines, but which Silicon Valley has little interest in accommodating if that means limiting what can be done (and how much money can be made). Utopia, we are told, is life without work, instructing BeerBot to fetch us a cold one while we lie on the couch watching Netflix. Come to think of it, why can’t BeerBot just anticipate that I need a cold one!

Baxter the Robot
Baxter the robot. Source: BBC News, which included the funny caption “Baxter can work happily alongside human co-workers.” We ask, can humans work happily alongside Baxter?

Back in the industrial world, automation has changed laborers and craftsmen into button pushers and monitors—caretakers making sure nothing goes wrong. But as Carr points out, automation is not just a threat to the blue collar workforce. White collar jobs that involve design, analysis and decision making are very much in the cross hairs. If corporations are willing to replace workers with robots, why would they hesitate to replace a multitude of managers with Mr. Algorithm? They won’t.

The effect of technology on employment is neither the point of Carr’s book nor the point of this post. I am more interested in the effect of (logistics) technology on us. Is the logistics industry developing machines and devices that improve the human condition, or is it developing machines and devices that improve ROI? Are these objectives mutually exclusive? Must they be?

What is really interesting to me is the prospect that, in an environment of scarce labor resources, companies that developed and implemented human-centric work environments with “human optimized automation”—perhaps at a higher cost—might have the last laugh. What exactly “human optimized automation” looks like is still an open question, but I am sure it doesn’t look like a row of buttons and toggle switches. Here’s hoping that Carr’s book gets a wide reading in our industry, and that suppliers and end-users in the logistics industry find a way to develop automation that serves rather than dehumanizes us.

The Physical Internet as Platform Innovation

FeaturedThe Physical Internet as Platform Innovation

I am writing from the MHI Annual Conference in Rancho Bernardo, California. This morning I attended a talk by Jim Rice from MIT on supply chain innovation. It was a thought provoking seminar that proposed a distinction between invention and innovation. He offered a definition of innovation that went something like, “combining existing technologies, processes, and information in new ways to deliver good and desirable outcomes.” The key—and I suppose slightly controversial—point is that innovation is a combination of existing things, rather than the creation of something new. He argues, for example, that the Kiva system is innovation rather than invention because the system is comprised of more or less already known technologies and processes.

Another point in his talk, following Christensen’s model of innovation, was to distinguish between sustaining and disruptive innovations. An easy illustration is the iPhone, which itself was a disruptive innovation; the fingerprint reading capability in the 5s was a sustaining innovation. One changes the game; the other continues the game.

Conceptual drawing of a Physical Internet hub
Conceptual drawing of a Physical Internet hub.

It occurred to me during the talk that another, higher class of innovation might be defined—call it platform innovation. Some innovations are more than disruptive—they serve as platforms for other disruptions in perhaps completely new areas. For example, the internet was a platform innovation in that it served as a platform for thousands of other disruptive innovations. The automobile could also be considered a platform innovation because it gave birth to the taxi industry, the racing industry, and even the logistics industry.

I contend that the Physical Internet (PI) would also be a platform innovation, should it come to pass, in that it provides a backbone of logistics services, processes, and information upon which one could easily imagine many new innovations arising. One of the slides in Ben Montreuil’s stump speech on the PI asks, what are the PI equivalents of Google, Yahoo, and Amazon?—all of which owe their existence to the platform innovation of the digital internet. In a PI world, it is easy to imagine that hundreds of new companies would spring up offering previously unimagined products and services, which is one reason the Physical Internet is so exciting to think about.

The flexconveyor module
The Flexconveyor by Gebhardt.

If the reader will indulge me, I believe the concept of plug and work material handling could also become a platform innovation someday.  The Flexconveyor and GridStore systems are just two manifestations of the simple idea that one ought to be able to plug material handling devices together in different configurations to perform different functions. I have long thought that new business models might spring up based on this kind of flexibility. For example, imagine a material handling rental company that delivers conveyor modules to customers just as they need them and then moves them elsewhere when the need expires (think seasonal distribution). Or how about trucks with self-organizing loads based on the GridStore architecture?

These developments will take time, of course. In the meantime there is much to do, both on the Physical Internet and on plug and work material handling.

A New Angle on Container Ports

FeaturedA New Angle on Container Ports

Goran Ivanović recently published an article entitled, “A different kind of container yard” in the journal World Port Development.  By “different kind,” he means layouts based on the fishbone and chevron aisle structures we have used for unit-load warehouses. (Goran is a former student whose own work produced insights into aisle designs for warehouses with multiple pickup and deposit points.) The article is difficult to find on the web, so if you’d like a copy, please contact Goran (address below).

Here’s what a little fresh thinking does to the traditional container port:

The chevron port design. Source: Ivanović Consultants.

For those unfamiliar with our previous work, diagonally arranging aisles, or in this case container stacks, allows vehicles (here, straddle carriers) to travel straight line distances when they otherwise would have to travel rectilinear distances (east-west, north-south). Reduced distance means higher productivity measured in containers moved per hour—presto, higher port throughput. The article also lists other benefits of the chevron arrangement, including improved storage density (I’ll let the reader ponder that one) and reduced rutting of pavement areas—I love this one!

Fishbone aisles in a container port. This design has lower expected travel cost, at the expense of slightly lower storage density. Source: Ivanović Consultants.

A fishbone design doesn’t fare as well on storage density, but it has better distance performance than the chevron and the traditional. As the article states, “new concepts offer the ability to trade space for travel distance and traffic speed, depending on what’s more important to an operator.” Just like the warehouse.

I probably don’t need to say this, but I’m thrilled to see this clever application of “non-rectilinear thinking” to a new domain. If Goran can deliver improved throughput to even one of the world’s international ports—many of which are operating at throughput capacity, by the way—he will have done a great service to the world economy (yes, I just said that). Ports really matter, and in my opinion, they are ripe for a revolution in design.

What would a full blown implementation of these ideas look like? Here is a graphic his firm generated:

A new kind of container port based on diagonal aisles. Source: Ivanović Consultants.

You get the idea, I trust.

This is probably a good place to mention that what looks like a simple insight is often more difficult to apply in practice than it appears. The exact dimensions and access points of a real port will differ from the graphics above, of course, so these designs should be considered conceptual. Russ Meller and I learned this with the original aisle design work, which was misapplied by more than one company that meant well. If only they had called us. …

Here’s hoping that someone in Singapore or Rotterdam or Long Beach sees this work and gives Goran a call. He can be reached at goran.ivanovic@yandex.ru. You can learn more about this work at his website.

First the warehouse, now the container port.

Rail yards, anyone?

[Correction: An earlier version of this post had “stacker crane” instead of “straddle carrier.” Yikes!]

The social implications of crowdsourced delivery

FeaturedThe social implications of crowdsourced delivery

Ben Montreuil recently tweeted a YouTube link to MyWays, DHL’s crowdsourced last mile delivery service in Stockholm. As I wrote recently in my DC Velocity blog, crowdsourcing companies are invading the logistics world like the “dot coms” of 1999. The innovations in this space are happening at breakneck speed—I was astonished to notice that the video was posted almost a year ago!

The MyWays video below features Carolina and Ola on both ends of a crowdsource transaction. Ola orders guitar strings and selects MyWays as his means of delivery. Carolina sees the delivery on her app and decides to make a few “credits” by delivering the strings on her way home from university.

Three quick features before I get to what is most interesting to me….

  1. Ola gets to specify both a location and a time window for his delivery. Presumably he could change this information over time, as his plans change for the day. This is a step toward “direct to device” delivery that we described in the U.S. Roadmap for Material Handling and Logistics, in which delivery drivers (we were thinking of package carrier drivers—silly us!) make deliveries to the location of people (read: their GPS-enabled devices) rather than to addresses. It won’t be long before someone tries this.
  2. Ola names his price, in units of “credits.” I love this feature! Absolutely, positively want it in the next hour? Then be willing to pay for it. Creating a real-time market for delivery pricing is an ingenious way to price a new service, and it absolves DHL of meeting service expectations. Don’t like the service you got? Then you were too cheap to pay for what you wanted!
  3. Carolina “pulls” her delivery, rather than MyWays pushing it to her. Again, this feature absolves DHL of making suboptimal or inappropriate assignments that the “drivers” themselves would be better off making. The disadvantage, of course, is the potential for missed opportunities. What if Carolina had forgotten to check her app when an easy delivery had been available? This could easily be fixed with optional push notifications.

What is most interesting to me, however, is the end of the video, in which Carolina and Ola meet face to face. There is just something appealing about the social implications of crowdsourcing. We all love our DHL drivers, but to customers they are just an extension of the corporation—and they wear uniforms for crying out loud! When someone from the neighborhood delivers my package, I make a social connection that I otherwise wouldn’t, and the experience itself enhances my quality of life. Now that is real value.

New Paper: Approximating Sojourn Times

Yet another announcement today!  (I am atoning for months of ignoring my blog.)  My former student Hyun Ho Kim and I are pleased to announce the publication of “An Approximation Model for Sojourn Time Distributions in Acyclic Multi-Server Queueing Networks” in Computers & Operations Research.

Queueing networks have been an attractive method of modeling complex manufacturing and other systems for many decades. Much of this work is limited in that it develops means for performance measures of interest rather than distributions, or it assumes exponential arrival or service processes. Our paper describes a mathematical model that produces a distribution for the sojourn time (total time in the system, including delays and processing), in the presence of general distributions for service processes.

Results of the model
Results of the model. On the left is the probability density function; on the right, the cumulative distribution function. From the plot on the right, an order has approximately 80% chance of being processed in less than 10 time units.

Here’s an example of how this research might be used in practice: Suppose you are interested in determining a cutoff time for accepting orders in an order fulfillment system, before which you guarantee the order will make it onto the last truck leaving in the evening. You have collected data on all the relevant order processing times—picking, transport to packing, packing, transport to shipping, and shipping. These data, of course, are variable, and you would like to assess the risk of setting a particular cutoff time in light of all this variability.

The model we develop in this paper takes the means and variances of all the relevant processing times and combines them to produce a distribution for the sojourn time of an order, so that you can make statements such as, “orders can be fulfilled within 2 hours with 98 percent probability,” or “orders can be fulfilled within 1 hour with 90 percent probability.” These values can then be used to determine an “optimal” cutoff time, such that the expected benefit of getting the order on the truck (revenue from premium shipping) just exceeds the cost of missing the truck (perhaps offering free shipping because the promise wasn’t kept). The tradeoff is “newsvendor like.”

Technical AbstractWe develop an approximation model for the sojourn time distribution of customers or jobs arriving to an acyclic multi-server queueing network. The model accepts general interarrival times and general service times, and is based on the characteristics of phase-type distributions. The model produces excellent results for multi-server networks with a small to medium number of workstations, but is less accurate when the number of workstations is large.

If you would like a copy of the paper, please email me.